Google DeepMind reported that its AlphaProof Nexus system resolved 9 of the 353 open Erdos problems it targeted and proved 44 of 492 open conjectures from the Online Encyclopedia of Integer Sequences, with each proof formally verified in the Lean proof assistant.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source 2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source The system pairs the Gemini 3.1 Pro model with Lean, which checks every logical step against mathematical axioms, and the work was documented in an arXiv preprint dated May 21, 2026 with proofs posted to GitHub.2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source The stake is epistemic: unlike a benchmark score, a Lean-verified proof cannot be inflated by test contamination or plausible-sounding but wrong reasoning. We assess with high confidence that these specific results are genuine and checkable, and with moderate confidence that they signal AI moving into narrow, verifiable mathematical discovery, not the broad reasoning leap the framing can invite.

Why verification changes the claim

Most AI capability claims rest on benchmarks, which are vulnerable to data leakage, overfitting, and answers that read as correct without being so. A formal proof in Lean is different in kind: the machine rejects any step that does not follow from the axioms, so a verified proof is correct by construction, not by human judgment of plausibility.2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source Fields Medal winner Timothy Gowers underlined the distinction, noting that these are machine-checked proofs rather than arguments that might contain errors.3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source That is the load-bearing fact of the whole story. When DeepMind says nine Erdos problems were solved, the claim is auditable in a way that a leaderboard position is not, because anyone can run the Lean checker over the published proofs.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source 3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source

The problems themselves were not trivial. Two of the nine had been open for 56 years, placing this well beyond the olympiad-style problems earlier systems handled, which talented humans can solve in hours.3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source Each solved problem cost a few hundred dollars in compute.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source 2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source 3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source That figure carries an important caveat the sources flag: it counts only verified successes and excludes the compute burned on abandoned search paths, so the true cost of discovery per result is higher than the sticker price.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source

What it means, and the honest limits

DeepMind was deliberate about scope. Leadership framed the result as a constrained research workflow, not general intelligence, and paired the announcement with the message that this is AI operating usefully inside a verified pipeline rather than a step toward AGI.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source The proportions support that restraint: 9 of 353 Erdos problems and 44 of 492 OEIS conjectures are real results but small fractions of the targeted sets, meaning the system is a powerful assistant on a subset of tractable problems, not a general solver.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source 2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source The authors' own framing, that formal proof search can deepen human understanding rather than replace it, points the same way.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source

Who gains and who loses is specific. Working mathematicians gain a tool that can clear certain long-standing but tractable conjectures cheaply and hand back auditable proofs, shifting scarce human attention to problems the machine cannot reach.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source 3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source DeepMind gains a rare capability claim that cannot be dismissed as benchmark gaming, which strengthens its position in the credibility contest among labs.2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source 3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source Rivals relying on unverifiable benchmark leads are pressured by comparison: one source notes OpenAI had solved a single Erdos conjecture, against DeepMind's nine with stronger formal guarantees, which reframes the competition around checkable results.3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source The party that should stay cautious is any reader who reads nine solved problems as evidence of general mathematical reasoning; the verification that makes the claim strong also makes it narrow, because Lean only certifies the specific proofs it checked.2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source

The counter-case

The strongest argument against reading this as genuine discovery is that verification proves correctness, not novelty or importance. A Lean-checked proof is definitely right, but the system could be clearing problems that were open for lack of attention rather than difficulty, in which case the achievement is efficient search over a known space rather than insight.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source The undisclosed cost of failed attempts matters here too: if the machine explores enormous numbers of dead ends to land nine successes, the result is closer to brute-force enumeration with a verifier than to mathematical understanding.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source For the discovery thesis to fail, the solved problems would have to turn out to be low-hanging by expert judgment, and the search cost per genuine advance to be so high that the method does not generalize to harder open questions.

What to watch

  • Mathematicians assess significance. Watch for working number theorists and combinatorialists to publicly judge, over the next one to two quarters, whether the nine solved problems were hard or merely neglected; their verdict, not the count, determines whether this is discovery.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source 3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source
  • Full search cost is disclosed. If DeepMind or independent replication reports the compute spent on failed paths, the true cost per result becomes clear; a low ratio of waste would strengthen the discovery claim, a high one would reframe it as expensive search.1 WinBuzzer 2026-05-26 AlphaProof Nexus resolved 9 of 353 open Erdos problems and 44 of 492 OEIS conjectures, verified in Lean; DeepMind framed it as a constrained research workflow, not AGI; the few-hundred-dollar cost excludes abandoned search paths. Open source
  • The method reaches harder problems. Track whether formally verified systems clear problems widely regarded as difficult, not just long-open, within the next year; success there would show generalization beyond the current tractable subset.2 CryptoBriefing 2026-05-25 System combines Gemini 3.1 Pro with Lean, which checks every logical step; solved 9 Erdos problems (~2.5%) and 44 OEIS conjectures (~9%) for a few hundred dollars each; documented in arXiv preprint 2605.22763v1 (May 21, 2026) with proofs on GitHub. Open source
  • Verification becomes a norm. Watch whether rival labs shift to publishing Lean-checked or otherwise formally verified results rather than benchmark scores for math claims; a move in that direction would confirm that auditability is becoming the standard the field rewards.3 FAQ.com.tw 2026-05-25 Two solved problems had been open 56 years; Fields Medal winner Timothy Gowers stressed the proofs are machine-checked, not plausible arguments; DeepMind's nine solutions with Lean output contrasted with OpenAI's single Erdos conjecture. Open source

The forward implication is that the most defensible AI claims are becoming the ones a third party can mechanically check. AlphaProof Nexus matters less for the nine problems than for demonstrating a template where a capability assertion comes with a proof anyone can run, which is a higher and harder bar than any leaderboard.